Question

ABCD is a rectangle formed by the points A(–1, –1), B(– 1, 4), C(5, 4) and D(5, – 1). P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.

Answer 1

Solution: Coordinates of P can be calculated as follows:

Coordinates of Q can be calculated as follows:

Coordinates of R can be calculated as follows:

Coordinates of S can be calculated as follows:

Length of PQ can be calculated as follows:

Similarly, QR can be calculated as follows:

The above values show that RS = PS, i.e. all sides are equal.

Now let us calculate the diagonals

Hence, it is clear that while all sides are equal, diagonals are not equal. So, the given figure is a rhombus.